how do you shut the computer down??
do you use the button on thew keyboard (e.g. key labeled "power" )
do you use the button on the case
do you use the "start menu -turn off computer-turn off" comand
i am assuming that you go through the start menu!!
the first place i would check is you properties
right click on desktop-properties-screensaver-power (at the bottom of that tab)-then go through all the options their.
also your bios may have settings like, wake on LAN, wake on mouse, wake on Keyboard e.g. set these may be causeing the computer to still be semi powered.